Abstract:
The Open Pit Mine Production Scheduling Problem (OPMPSP) studied in
recent years is usually based on a single geological estimate of
material to be excavated and processed over a number of decades.
However techniques have now been developed to generate multiple
stochastic geological estimates that more accurately describe the
uncertain geology. While some attempts have been made to use such
multiple estimates in mine production scheduling, none of these
allow mining and processing decisions to flexibly adapt over time,
in response to observation of the geological properties of the
material mined. In this paper, we use multiple geological estimates
in a mixed integer multistage stochastic programming approach, in
which decisions made in later time periods can depend on
observations of the geological properties of the material mined in
earlier periods. Since the material mined in earlier periods is
determined by our decisions, the information received about
uncertain properties, and when that information is available, is
decision-dependent. Thus we tackle the difficult case of stochastic
programming with endogeneous uncertainty. We extend a successful
mixed integer programming formulation of the OPMPSP to this
stochastic case, and show that non-anticipativity can be modelled
with linear constraints involving variables already present in the
model. We extend this observation to the general class of endogenous
stochastic programs, and exploit the special structure of our model
to show that in some cases we can omit a significant proportion of
these constraints. Using data supplied by our industry partner, (a
multinational mining company), we show that this approach is
reasonably tractable, and demonstrate the improvements that can be
made to mine schedules through the explicit use of multiple
geological estimates.